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Frontiers of Mechanical Engineering

Front. Mech. Eng.    2015, Vol. 10 Issue (3) : 277-286     https://doi.org/10.1007/s11465-015-0348-8
RESEARCH ARTICLE |
Fault diagnosis of spur gearbox based on random forest and wavelet packet decomposition
Diego CABRERA1,2,*(),Fernando SANCHO2,René-Vinicio SÁNCHEZ1,Grover ZURITA1,3,Mariela CERRADA1,4,Chuan LI1,5,Rafael E. VÁSQUEZ6
1. Departamento de Ingeniería Mecánica, Universidad Politécnica Salesiana, Cuenca, Ecuador
2. Departamento de Ciencias de la Computación e Inteligencia Artificial, Universidad de Sevilla, España
3. Departamento de Ingeniería Electro-Mecánica, Universidad Privada Boliviana, Cochabamba, Bolivia
4. Departamento de Sistemas de Control, Universidad de Los Andes, Mérida, Venezuela
5. Research Center of System Health Maintenance, Chongqing Technology and Business University, Chongqing 400067, China
6. Facultad de Ingeniería Mecánica, Universidad Pontificia Bolivariana, Medellín, Colombia
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Abstract

This paper addresses the development of a random forest classifier for the multi-class fault diagnosis in spur gearboxes. The vibration signal’s condition parameters are first extracted by applying the wavelet packet decomposition with multiple mother wavelets, and the coefficients’ energy content for terminal nodes is used as the input feature for the classification problem. Then, a study through the parameters’ space to find the best values for the number of trees and the number of random features is performed. In this way, the best set of mother wavelets for the application is identified and the best features are selected through the internal ranking of the random forest classifier. The results show that the proposed method reached 98.68% in classification accuracy, and high efficiency and robustness in the models.

Keywords fault diagnosis      spur gearbox      wavelet packet decomposition      random forest     
Corresponding Authors: Diego CABRERA   
Online First Date: 09 September 2015    Issue Date: 23 September 2015
 Cite this article:   
Diego CABRERA,Fernando SANCHO,René-Vinicio SÁNCHEZ, et al. Fault diagnosis of spur gearbox based on random forest and wavelet packet decomposition[J]. Front. Mech. Eng., 2015, 10(3): 277-286.
 URL:  
http://journal.hep.com.cn/fme/EN/10.1007/s11465-015-0348-8
http://journal.hep.com.cn/fme/EN/Y2015/V10/I3/277
Fig.1  Training process for the RF classifier
Fig.2  Test process for the RF classifier
Fig.3  Configuration of system for failure’s simulation
Fig.4  Feature extraction process. (a) WPD; (b) energy extraction and features vector building
Mother wavelets oob-error Feature’s number Tree’s number
db7 0.0590 12 1901
db7+sym3 0.0419 8 1713
db7+sym3+coif4 0.0410 7 1671
db7+sym3+coif4+bior6.8 0.0390 17 727
db7+sym3+coif4+bior6.8+rbior6.8 0.0438 10 1191
Tab.1  The best selected wavelets and the best model parameters
Fig.5  Curves of training: (a) oob-error for each set of wavelets with variable number of random features; (b) oob-error for the set of the best wavelets for maximum randomness (1), maximum correlation (256) and perfect randomness (17) with a variable number of trees
Fig.6  Selection of features: (a) Importance of features without selection; (b) importance of features with selection; (c) curve of further training to the selection of features
Class 1 2 3 4 5 6 7
1 37 0 0 0 0 0 0
2 0 37 0 0 0 0 0
3 0 3 34 1 0 0 0
4 0 0 2 35 1 0 0
5 0 0 0 0 38 0 0
6 0 0 0 0 0 36 1
7 0 0 0 0 0 0 37
Tab.2  Confusion matrix
Metric Value/%
Accuracy 96.950
Sensibility 97.000
F score 96.975
Tab.3  Classifier’s performance measures
Class 2 3 4 5 6 7
1 100 100 100 100 100 100
2 96.05 100 100 100 100
3 96.3 100 100 100
4 98.68 100 100
5 100 100
6 98.65
Tab.4  AUC individual unit: %
Fig.7  Separation of samples. (a) Location of samples; (b) coordinates eigen-values
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